"Not designed for it" is a 4-word summary of the basic problem: headlamps and fog lamps are optical devices engineered to a high degree of precision, and requiring a high level of system precision in order to work appropriately. This applies even to lamps regarded as poor. These lamps have a complicated task to achieve: they have to put the right amounts of light in the right places, which means very high intensity light (for seeing) very close to very low intensity light (for glare control). They can't just put out a random spray of light, even if that's what it might look like they do when you shine them on a wall. The optics in these lamps are a type known as "imaging optics" -- they magnify, superimpose/overlap, expand, contract, shift, rotate, and align images of the light source to build up the overall beam pattern. The exact distribution of these images depends on the light source being of a very specific, particular size, shape, position and orientation, exactly as originally engineered, and it has to match
all of those aspects. No matter how closely one light source's position matches another light source's position, if the two light sources aren't also the same size, shape, and orientation, the headlamp won't work right. The images won't be as intended, so the optical transformations of the images won't be as intended, so the beam pattern won't be as intended, so the wrong amounts of light will be sent to the wrong locations, and it can't be compensated by adjusting the lamp aim.
There's good information on
this page. The optical-level details are different for HID and LED, but the explanations hold good. There's also a very good recent SAE paper on the subject, with lots of images and data from actual experiments; that's available for purchase
here.